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216 CHAPTER 6 / EXTERNAL MEMORY

locations by reading from the source track into the main memory buffer and then
writing the date from the buffer to the target track.
a. How long will it take to transfer sector 1 on track 8 to sector 1 on track 9?
b. How long will it take to transfer all the sectors of track 8 to the corresponding sec-
tors of track 9?
6.7 It should be clear that disk striping can improve data transfer rate when the strip size
is small compared to the I/O request size. It should also be clear that RAID 0 pro-
vides improved performance relative to a single large disk, because multiple I/O re-
quests can be handled in parallel. However, in this latter case, is disk striping
necessary? That is, does disk striping improve I/O request rate performance com-
pared to a comparable disk array without striping?
6.8 Consider a 4-drive, 200GB-per-drive RAID array. What is the available data storage
capacity for each of the RAID levels, 0, 1, 3, 4, 5, and 6?
6.9 For a compact disk, audio is converted to digital with 16-bit samples, and is treated a
stream of 8-bit bytes for storage. One simple scheme for storing this data, called direct
recording, would be to represent a 1 by a land and a 0 by a pit. Instead, each byte is
8
expanded into a 14-bit binary number. It turns out that exactly 256 (2 ) of the total of
14
16,134 (2 ) 14-bit numbers have at least two 0s between every pair of 1s, and these
are the numbers selected for the expansion from 8 to 14 bits. The optical system de-
tects the presence of 1s by detecting a transition for pit to land or land to pit. It detects
0s by measuring the distances between intensity changes. This scheme requires that
there are no 1s in succession; hence the use of the 8-to-14 code.
The advantage of this scheme is as follows. For a given laser beam diameter,
there is a minimum-pit size, regardless of how the bits are represented. With this
scheme, this minimum-pit size stores 3 bits, because at least two 0s follow every 1.
With direct recording, the same pit would be able to store only one bit. Considering
both the number of bits stored per pit and the 8-to-14 bit expansion, which scheme
stores the most bits and by what factor?
6.10 Design a backup strategy for a computer system. One option is to use plug-in external
disks, which cost $150 for each 500 GB drive.Another option is to buy a tape drive for
$2500, and 400 GB tapes for $50 apiece. (These were realistic prices in 2008.) A typi-
cal backup strategy is to have two sets of backup media onsite, with backups alter-
nately written on them so in case the system fails while making a backup, the previous
version is still intact. There’s also a third set kept offsite, with the offsite set periodi-
cally swapped with an on-site set.
a. Assume you have 1 TB (1000 GB) of data to back up. How much would a disk
backup system cost?
b. How much would a tape backup system cost for 1 TB?
c. How large would each backup have to be in order for a tape strategy to be less
expensive?
d. What kind of backup strategy favors tapes?